matlab求矩阵的特征值与特征向量介绍.doc

使用matlab求矩阵的特征值和特征向量介绍

[v,d]=eig(A);
A为你的矩阵，V为特征向量矩阵，D为特征值矩阵，然后对D求最大值即可得最大特征根！
[V,D]=EIG(X)producesadiagonalmatrixDofeigenvaluesandafullmatrixVwhosecolumnsarethecorrespondingeigenvectorssothatX*V=V*D.V是特征向量，D是特征值
实例：
矩阵：12/37/37/33/213/23/23/72/313/23/72/32/31

>>formatrat>>A=[12/37/37/33/213/23/23/72/313/23/72/32/31]A=12/37/37/33/213/23/23/72/313/23/72/32/31>>[V,D]=eig(A)V=1793/2855504/3235-146/235i504/3235+146/235i1990/4773670/1079-3527/5220-3527/5220-509/9594350/119891160/4499+287/3868i1160/4499-287/3868i-350/647838/2819181/3874+1179/4852i181/3874-1179/4852i1238/2467D=810/1970000-93/4229+455/674i0000-93/4229-455/674i0000-149/2201
如何归一化求权重呢？
>>a=[135;1/313;1/51/31]
a=
1.00003.00005.00000.33331.00003.00000.20000.33331.0000
>>[V,D]=eig(a)
V=
0.91610.91610.91610.3715-0.1857+0.3217i-0.1857-0.3217i0.1506-0.0753-0.1304i-0.0753+0.1304i
D=
3.0385000-0.0193+0.3415i000-0.0193-0.3415i
**************************************************************************
>>a=[1248668;1/2126448;1/41/214246;1/81/61/41224;1/61/41/21/2114;1/61/41/41/2112;1/81/81/61/41/41/21]
a=
1.00002.00004.00008.00006.00006.00008.00000.50001.00002.00006.00004.00004.00008.00000.25000.50001.00004.00002.00004.00006.00000.12500.16670.25001.00002.00002.00004.00000.16670.25000.50000.50001.00001.00004.00000.16670.25000.25000.50001.00001.00002.00000.12500.12500.16670.25000.25000.50001.0000
>>rats(a)
ans=
12486681/21264481/41/2142461/81/61/412241/61/41/21/21141/61/41/41/21121/81/81/61/41/41/21
>>[V,D]=eig(a)
V=
0.78840.83270.83270.80830.8083-0.5119+0.3865i-0.5119-0.3865i0.48940.3216+0.2636i0.3216-0.2636i0.1760+0.0792i0.1760-0.0792i0.67830.67830.30380.0883+0.2728i0.0883-0.2728i-0.4630+0.1038i-0.4630-0.1038i-0.2011-0.2400i-0.2011+0.2400i0.1404-0.1620+0.1018i-0.1620-0.1018i0.0620-0.0510i0.0620+0.0510i-0.0006+0.1021i-0.0006-0.1021i0.1215-0.0627-0.0658i-0.0627+0.0658i0.0367+0.2360i0.0367-0.2360i-0.0531+0.0357i-0.0531-0.0357i0.0975-0.0303-0.0476i-0.0303+0.0476i0.0488-0.1148i0.0488+0.1148i0.0231-0.1221i0.0231+0.1221i0.0